Answer:
2. degree 3; leading coefficient 8
4. degree 6; leading coefficient 7
6. not a polynomial
Step-by-step explanation:
The "leading coefficient" is the coefficient of the highest-degree term in the sum of terms that makes up a polynomial.
These expressions all have one variable, so the number of variables in not an issue in any case. All of the exponents are positive integers, so that is not an issue in any case. However, the variable appears in the denominator in the expression of problem 6, so that sum is not a polynomial.
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2. In order to put this into the form we recognize as a polynomial, the expression must be "simplified' by performing the multiplication of the two factors:
= 8x³ -4x² +6x -3
The leading coefficient is the coefficient of the highest-degree term, which is the product of the highest-degree terms of the factors. That product is ...
(2x)(4x²) = 8x³
so the leading coefficient is 8. The variable is to the 3rd power, so the degree is 3.
You don't actually have to do the rest of the multiplication in order to find the required answer.
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4. The expression is already written as a sum, so we only need to find the term of highest degree. That is the last one: 7y^6. Its degree is 6 and its leading coefficient is 7.
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6. Variables are not allowed in the denominator of a polynomial. This expression is not a polynomial.
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<em>Comment on degree</em>
The degree of a term is the exponent of the variable. If there is more than one variable, the degree of the term is the sum of their exponents. For example, the polynomial ...
x² +xy +y²
has three terms, each of degree 2.
If this example were one of your problems, it would be rejected as "not a polynomial in one variable," since two variables are involved.
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